Showing 1200 entries on a page could be an issue. Though not really a Connections issue. If you tried displaying 1200 WordPress page/post title on a single page that would have the same impact. Maybe even more.
As a test on my host (with a limit of 1200 since I have 30K in my Connections db and all those can not be listed on a single page):
- PHP 5.3.29 takes about 11 seconds to load using 140MB of memory.
- PHP 7.0.3 takes about 2.5 seconds to load using 53MB of memory.
What can you take from that, I guess not to much really because I really have no idea on the impact of virtual memory, not being a server admin. But I do know that a whole host of things can contribute the server resource usage down to how the host is configured to what software version they are using. One example is PHP7 which is far, far, more memory efficient and much faster.
I see you are using Super Cache. It says the page is created in about 10 seconds. Make sure to use a longer cache expiration time, maybe 24 hours, that way the page is only created once a day. That will definitely reduce server resource usage since the page would only be created one a day.
Not sure if that is of any help, hope it is.